The item that appears in red text in a dictionary entry matches the form of a word you have searched for. If that word is the headword, then that will be in red. For example, if you search on the term ‘eye’ then the headword ‘eye’ will appear in red.
The left-hand section lists entries where the term appears either as the headword (eye), as part of the headword (apple of the eye), as part of a phrase definition (blink — in the blink of an eye), or as a variant. When you click on any of these results, ‘eye’ will show in red to highlight its position, making it easier to locate within an entry.
Similarly, in the thesaurus, the red text helps you find a word within the strings of synonyms. After clicking in the left-hand section on the keyword that best suits the sense you are after, the red text highlights the position of your search term.